Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-2x+y &= -4 \\ -5x+y &= -8\end{align*}$
Begin by moving the $x$ -term in the second equation to the right side of the equation. $y = {5x-8}$ Substitute this expression for $y$ in the first equation. $-2x+({5x - 8}) = -4$ $-2x + 5x - 8 = -4$ Simplify by combining terms, then solve for $x$ $3x - 8 = -4$ $3x = 4$ $x = \dfrac{4}{3}$ Substitute $\dfrac{4}{3}$ for $x$ back into the top equation. $-2( \dfrac{4}{3})+y = -4$ $-\dfrac{8}{3}+y = -4$ $y = -\dfrac{4}{3}$ $y = -\dfrac{4}{3}$ The solution is $\enspace x = \dfrac{4}{3}, \enspace y = -\dfrac{4}{3}$.